In a medium saucepan, melt the butter over medium heat. Add the flour and whisk together to form a paste. Cook for 1 minute while whisking continuously. Remove from the heat.
Add 1/4 cup of the milk and whisk until smooth. Repeat adding a little bit of milk at a time, whisking until smooth with each addition, until all of the milk is added.
Increase heat to medium-high and bring to a boil while whisking constantly. Let simmer one minute and then take off the heat. The sauce has the right consistency when it will coat the back of a spoon.
Season with salt, pepper and nutmeg to taste or as desired.
You can jazz this recipe up by adding shallots, onions, or even a little Parmesan cheese to give it a little more flavor and kick.